What people seem to forget is that not all anarchist agree that direct democracy is good or desirable. Individualist anarchists are famous for criticizing democracy since it can ignore the rights of the minority. For every syndicalists and council communist who thinks democracy is a good idea, you have other libertarians and anarchists who see democracy as a form of control. The problem with the definition of anarchism that states ' self-governed societies with voluntary institutions' is that it doesn't specifically define to what extent a society is self-governed and at what point does voluntarily working together become coercion. Max Stirner is known by many as "name appears with familiar regularity in historically orientated surveys of anarchist thought as one of the earliest and best known exponents of individualist anarchism". He created a branch of anarchism called egoist anarchism that wanted to "abolish not only the state but also society as an institution responsible for its members". He also believed you should be able to take what you wanted if you had the power to take it, even if the democratic members of a society said otherwise:
"I do not step shyly back from your property, but look upon it always as my property, in which I respect nothing. Pray do the like with what you call my property! [...] What I have in my power, that is my own. So long as I assert myself as holder, I am the proprietor of the thing; [...]. Whoever knows how to take, to defend, the thing, to him belongs property" - Stirner, Max. The Ego and Its Own
There is also insurrectionary anarchism, a form of individualist anarchism that says any individual should be allowed to engage and violence against any system they don't like in a form of 'permanent class conflict', even if most people agree to be there voluntarily:
Revolution and insurrection must not be looked upon as synonymous. The former consists in an overturning of conditions, of the established condition or status, the State or society, and is accordingly a political or social act; the latter has indeed for its unavoidable consequence a transformation of circumstances, yet does not start from it but from men's discontent with themselves, is not an armed rising, but a rising of individuals, a getting up, without regard to the arrangements that spring from it. The Revolution aimed at new arrangements; insurrection leads us no longer to let ourselves be arranged, but to arrange ourselves, and sets no glittering hopes on 'institutions'. It is not a fight against the established, since, if it prospers, the established collapses of itself; it is only a working forth of me out of the established. If I leave the established, it is dead and passes into decay. Now, as my object is not the overthrow of an established order but my elevation above it, my purpose and deed are not a political or social but (as directed toward myself and my ownness alone) an egoistic purpose and deed. - Max Stirner, The Ego and Its Own
"the anti-syndicalist anarchist-communists, who in France were grouped around Sébastien Faure's Le Libertaire. From 1905 onwards, the Russian counterparts of these anti-syndicalist anarchist-communists become partisans of economic terrorism and illegal 'expropriations'." -""Anarchist-Communism" by Alain Pengam describing insurrectionist anarchists
As someone stated above, "In an anarchy, however, taking part in community institution is voluntary. People don't have to follow any rules they don't agree with." With a direct democracy, you have to make sure everyone, including individualist anarchists who see the only society that they should listen to is their own ego or personal morality, follows the rules the society agrees on & doesn't simply ignore what the group voted for. For example, an individualist anarchist might ignore a democratic vote for everyone to get a standard education as anarchist thinkers " such as William Godwin (Political Justice) and Max Stirner ("The False Principle of Our Education") attacked both state education and private education as another means by which the ruling class replicate their privileges" and Francisco Ferrer opposed established education. Thus, you have a bunch of people who will refuse to give their child a proper education and see any attempt to provide standardized testing to see what children have learned as 'tyranny' and in a voluntary anarchist society, you can't just make a person get a proper education without their consent, leading to a constant problem of hyper-individualistic people fighting against the will of the community.